Too Long; Didn't Read

Messrs. Editors:—I have hesitated about the propriety of replying to the criticisms of your correspondent, J. E. Hendricks, upon my paper, on the action of the reciprocating parts of steam engines. It is not to be expected that a truth so opposed to commonly received notions—the reception of which requires so much to be unlearned—should at once receive the assent of every one. Some odd fancies on the subject are likely to be ventilated first. But your correspondent touches the root of the matter, and perhaps the fact questioned by him should be more clearly placed beyond dispute. I will dismiss the introductory part of his letter, merely observing that his "logical inference" is quite gratuitous and unwarranted. He says himself that its absurdity is obvious, in which I quite agree with him. The real question is this: What is the figure representing the acceleration of the motion of a piston, controlled by a crank which revolves with a uniform velocity? I stated it to be a right-angled triangle, and indicated, as I supposed, clearly enough, a simple method by which this could be shown. Your correspondent claims that the calculation, according to my own rule, gives a figure of a totally different form, and one that shows the acceleration, as well as the motion, to be reduced to zero at the commencement of the stroke. Let us see. Let the straight line, AJ, in the following figure, represent half the stroke of the piston, and let the distances, AB, AC, etc., on this line, represent the versed sines of 10°, 20°, etc., up to 90°, or the motion of the piston while the crank is moving through these arcs. At the points A, B, C, etc., erect the perpendiculars, Aa, Bb, Cc, etc., and let the length of each of these ordinates represent the acceleration imparted in a given time at that point of the stroke. Then will AJ be to Aa as IJ is to Ii, as HJ is to Hh, etc., showing that the straight line, aJ, connects the extremities of all the ordinates, and that the triangle, AJa, repr